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$T_{2}(T)$的几乎可裂序列及几乎$\mathcal {D}$-可裂序列
引用本文:张玉林,姚海楼.$T_{2}(T)$的几乎可裂序列及几乎$\mathcal {D}$-可裂序列[J].数学研究及应用,2013,33(1):11-22.
作者姓名:张玉林  姚海楼
作者单位:北京工业大学应用数理学院, 北京 100124;北京工业大学应用数理学院, 北京 100124
基金项目:国家自然科学基金(Grant No.10971172); 北京市自然科学基金(Grant Nos.1092002; 1122002).
摘    要:The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and D-split sequences. So in order to study the representations of triangular matrix algebra T2 (T ) = T0TT where T is a finite dimensional algebra over a field, it is important to determine its AR-sequences and D-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and D-split sequences of T2 (T) through the corresponding morphisms and sequences of T. Some interesting results are obtained.

关 键 词:algebras  modules  triangular  matrix  algebras  AR  sequences  approximations.
收稿时间:2011/7/15 0:00:00
修稿时间:2011/10/31 0:00:00

The Almost Split Sequences and ${\cal D}$-Split Sequences of $T_{2}(T)$
Yulin ZHANG and Hailou YAO.The Almost Split Sequences and ${\cal D}$-Split Sequences of $T_{2}(T)$[J].Journal of Mathematical Research with Applications,2013,33(1):11-22.
Authors:Yulin ZHANG and Hailou YAO
Institution:College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China;College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China
Abstract:The AR-quiver and derived equivalence are two important subjects in the representation theory of finite dimensional algebras, and for them there are two important research tools-AR-sequences and ${\cal D}$-split sequences. So in order to study the representations of triangular matrix algebra $T_{2}(T)=\begin{pmatrix} T & 0 \\ T & T \\ \end{pmatrix}$ where $T$ is a finite dimensional algebra over a field, it is important to determine its AR-sequences and ${\cal D}$-split sequences. The aim of this paper is to construct the right(left) almost split morphisms, irreducible morphisms, almost split sequences and ${\cal D}$-split sequences of $T_{2}(T)$ through the corresponding morphisms and sequences of $T$. Some interesting results are obtained.
Keywords:algebras  modules  triangular matrix algebras  AR sequences  approximations  
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